MathubLearn / Practice / Excel
Montana State University · Fall 2026 · math

M171 Calculus I: study guide

Limits, derivatives, integrals and everything in between, section by section from Active Calculus. Every topic below is a free study page; the same material lives in the Mathub app with practice, flashcards, the calendar and a grade calculator for this class.

MeetsMon · Wed · Fri lecture, plus one lab (Tue or Thu)
Credits4
Topics26

Exams and major deadlines

ExamWhenCovers
Exam 1Fri, Sep 18, 2026through §1.6 and Lab 3
Exam 2Fri, Oct 16, 2026through §2.6 (emphasis §1.7 – §2.6)
Exam 3Fri, Nov 6, 2026through §3.1 and §3.5 (emphasis §2.7, §2.8, §3.1, §3.5)
Exam 4Wed, Dec 9, 2026through §5.2 (emphasis §3.3 – §5.2)
Final ExamFinals week (Dec 14 – 18), day and time TBDcumulative, through §5.2

What Mathub gives you for M171

Open Calc I in MathubClass calendar

Unit 1: Understanding the derivative

  1. §1.1How do we measure velocity?
  2. §1.2The notion of limit
  3. §1.3The derivative of a function at a point
  4. §1.4The derivative function
  5. §1.5Interpreting, estimating, and using the derivative
  6. §1.6The second derivative

Unit 2: Computing derivatives

  1. §1.7Limits, continuity, and differentiability
  2. §1.8The tangent line approximation
  3. §2.1Elementary derivative rules
  4. §2.2Sine and cosine
  5. §2.3Product and quotient rules
  6. §2.4Derivatives of other trigonometric functions
  7. §2.5The chain rule
  8. §2.6Derivatives of inverse functions

Unit 3: Implicit, limits & extrema

  1. §2.7Implicit differentiation
  2. §3.5Related rates
  3. §2.8L'Hôpital's rule and limits at infinity
  4. §3.1Using derivatives to identify extreme values

Unit 4: Optimization & the integral

  1. §3.3Global optimization
  2. §3.4Applied optimization
  3. §4.1Determining distance traveled from velocity
  4. §4.2Riemann sums
  5. §4.3The definite integral
  6. §4.4The Fundamental Theorem of Calculus
  7. §5.1Constructing accurate graphs of antiderivatives
  8. §5.2The second Fundamental Theorem of Calculus